%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM684^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:18:32 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 19 unt; 0 typ; 2 def)
% Number of atoms : 46 ( 26 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 90 ( 16 ~; 11 |; 0 &; 60 @)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: nat ).
thf(func_def_1,type,
y: nat ).
thf(func_def_2,type,
z: nat ).
thf(func_def_3,type,
pl: nat > nat > nat ).
thf(func_def_8,type,
inv_pl_1: nat > nat > nat ).
thf(f1,axiom,
( ( pl @ z @ x )
= ( pl @ z @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i) ).
thf(f2,axiom,
! [X0: nat,X2: nat,X1: nat] :
( ( ( pl @ X0 @ X2 )
= ( pl @ X1 @ X2 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz20b) ).
thf(f3,axiom,
! [X1: nat,X0: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).
thf(f4,conjecture,
x = y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz20e) ).
thf(f5,negated_conjecture,
x != y,
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
! [X1: nat,X0: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
x != y,
inference(flattening,[],[f5]) ).
thf(f8,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( pl @ X0 @ X2 )
!= ( pl @ X1 @ X2 ) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f2]) ).
thf(f9,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( pl @ X1 @ X0 )
!= ( pl @ X2 @ X0 ) )
| ( X1 = X2 ) ),
inference(rectify,[],[f8]) ).
thf(f10,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(rectify,[],[f6]) ).
thf(f11,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( pl @ X1 @ X0 )
!= ( pl @ X2 @ X0 ) )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f13,plain,
( ( pl @ z @ x )
= ( pl @ z @ y ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f14,plain,
x != y,
inference(cnf_transformation,[],[f7]) ).
thf(f16,definition,
( spl0_1
<=> ( ( pl @ z @ x )
= ( pl @ z @ y ) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f18,plain,
( ( ( pl @ z @ x )
= ( pl @ z @ y ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f19,plain,
spl0_1,
inference(avatar_split_clause,[],[f13,f16]) ).
thf(f21,definition,
( spl0_2
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f23,plain,
( ( x != y )
| spl0_2 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f24,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f14,f21]) ).
thf(f25,plain,
! [X0: nat,X1: nat] :
( ( inv_pl_1 @ X0 @ ( pl @ X1 @ X0 ) )
= X1 ),
inference(injectivity,[],[f11]) ).
thf(f33,plain,
! [X0: nat,X1: nat] :
( ( inv_pl_1 @ X0 @ ( pl @ X0 @ X1 ) )
= X1 ),
inference(superposition,[],[f25,f12]) ).
thf(f49,plain,
( ( x
= ( inv_pl_1 @ z @ ( pl @ z @ y ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f33,f18]) ).
thf(f50,plain,
( ( x = y )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f49,f33]) ).
thf(f51,plain,
( $false
| ~ spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f50,f23]) ).
thf(f52,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[],[f51]) ).
cnf(s1,plain,
spl0_1,
inference(sat_conversion,[],[f19]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f24]) ).
cnf(s4,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f52]) ).
cnf(s5,plain,
~ spl0_1,
inference(rat,[],[s4,s2]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5]) ).
thf(f53,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM684^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n008.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 12:38:24 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.28 % (3085239)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (3085247)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3851015855:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.28 % (3085247) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3085239-3085247"...
% 0.21/0.28 % (3085247)...printing done.
% 0.21/0.28 % (3085247)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (3085247)------------------------------
% 0.21/0.28 % (3085247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (3085247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (3085247)CaDiCaL version: 2.1.3
% 0.21/0.28 % (3085247)Termination reason: Refutation
% 0.21/0.28 % (3085247)Time elapsed: 0.002 s
% 0.21/0.28 % (3085247)Peak memory usage: 13 MB
% 0.21/0.28 % (3085247)Instructions burned: 3 (million)
% 0.21/0.28 % (3085239)Success in time 0.038 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------